Discussion of article "Fundamentals of Statistics"
Oh I like the basics, they are like axioms. On a solid foundation - a solid"grail" ))
A couple of points that I didn't find answers to in the article on basics:
1) Why the sample expectation estimate is the arithmetic mean and not the geometric mean, the harmonic mean, or even the median. What is the rationale for this choice ?
2) Why is it necessary to calculate dispersion instead of mean absolute deviation if we want to know"how far the sample values are from its mathematical expectation "?
3) There is an interesting three in the kurtosis coefficient, which can make a bit of a mess if the coefficient is in the denominator. For the sake of what convenience it was put there ?
P.S. This is not a criticism of the article, but just for those who are learning the basics.
By the way, I too have always wondered how the standard deviation is better than the absolute mean. Does it have some other statistical properties? Or is all this squaring just because there is no function in maths to take the modulus in analytical form? )))
Perhaps these are just properties of the algebra of our space? Although here's found an article that directly answers the question -http://statanaliz.info/teoriya-i-praktika/10-variatsiya/15-dispersiya-standartnoe-otklonenie-koeffitsient-variatsii.html:
Standard deviation obviously also characterises a measure of data dispersion, but now (unlike dispersion) it can be compared to the original data, since their units are the same (this is evident from the calculation formula). But even this indicator in its pure form is not very informative, as it contains too many intermediate calculations that are confusing (deviation, squared, sum, mean, root).
Nevertheless, you can already work directly with the standard deviation, because the properties of this indicator are well studied and known. For example, there is the rule of three sigma, which states that in data with a normal distribution 997 values out of 1000 will be no further than 3 sigmas to one side or the other from the mean value.
Sigma, as a measure of uncertainty, is also involved in many statistical calculations. It is used to establish the degree of accuracy of various estimates and predictions. If the variation is very large, the standard deviation will also be large, hence the forecast will be inaccurate, which is expressed, for example, in very wide confidence intervals.
- statanaliz.info
By the way, I too have always wondered how standard deviation is better than absolute mean.
Oh I like the basics, they are like axioms. On a solid foundation - a solid "grail" ))
A couple of points that I didn't find answers to in the article on basics:
1) Why the sample expectation estimate is the arithmetic mean and not the geometric mean, the harmonic mean, or even the median. What is the rationale for this choice ?
2) Why is it necessary to calculate dispersion instead of mean absolute deviation if we want to know"how far the sample values are from its mathematical expectation "?
3) There is an interesting three in the kurtosis coefficient, which can make a bit of a mess if the coefficient is in the denominator. For the sake of what convenience it was put there ?
P.S. This is not a criticism of the article, but just a thought for those who are learning the basics.
1,2) Some mathematical calculations explaining the use of arithmetic mean and standard deviation - http://teorver-online.narod.ru/teorver49.html .
3) All parameter estimates given in this paper are unbiased. Therefore, there are all sorts of additive coefficients by which the estimation values must be multiplied (in particular, the triple from the kurtosis formula).
- teorver-online.narod.ru
We know all this, tell us how to build a grail out of it ))).
Unfortunately, another rewrite of elementary platitudes from a maths reference book. From the author's only some inaccuracies. Therefore, it is better to use the reference book than such articles.
Usually used quadratic error norms follow from their successful application in physics, because almost all sums of distributions in the limit of large numbers tend to the Gaussian distribution of random variables, which has exactly the square of error in the exponent. In this case, the probability of joint distribution of independent Gaussian distributed quantities contains the sum of squares of errors in the exponent.
Other error norms are quite admissible.
Other standards of error are perfectly acceptable.
Oh, that's interesting. Too bad my statistics textbook didn't mention it.
Maybe you also know how to recognise a polymodal distribution?
Maybe you also know how to recognise a polymodal distribution?
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New article Fundamentals of Statistics is published:
Every trader works using certain statistical calculations, even if being a supporter of fundamental analysis. This article walks you through the fundamentals of statistics, its basic elements and shows the importance of statistics in decision making.
What is statistics? Here is the definition found on Wikipedia: "Statistics is the study of the collection, organization, analysis, interpretation, and presentation of data." (Statistics). This definition suggests three main components of statistics: data collection, measurement and analysis. Data analysis appears to be especially useful for a trader as information received is provided by the broker or via a trading terminal and is already measured.
Modern traders (mostly) use technical analysis to decide whether to buy or sell. They deal with statistics in virtually everything they do when using a certain indicator or trying to predict the level of prices for the upcoming period. Indeed, a price fluctuation chart itself represents certain statistics of a share or currency in time. It is therefore very important to understand the basic principles of statistics underlying the majority of mechanisms that facilitate the decision making process for a trader.
Author: QSer29